On the linear static output feedback problem: the annihilating polynomial approach
| Autor: | Hariharan Narayanan, H. Narayanan |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Signal Processing (eess.SP)
Numerical Analysis Pure mathematics Polynomial Algebra and Number Theory Rank (linear algebra) Dynamical system Linear dynamical system LTI system theory Matrix (mathematics) Simple (abstract algebra) Optimization and Control (math.OC) FOS: Electrical engineering electronic engineering information engineering FOS: Mathematics Discrete Mathematics and Combinatorics 15A03 15A04 15A18 93B52 93B55 93C05 93C35 93D99 Geometry and Topology Electrical Engineering and Systems Science - Signal Processing Mathematics - Optimization and Control Eigenvalues and eigenvectors Mathematics |
| DOI: | 10.48550/arxiv.1810.11609 |
| Popis: | One of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback. We are given a linear dynamical system defined through \begin{align*} \mydot{w} &= Aw + Bu y &= Cw . \end{align*} The problem is to find, if it exists, a feedback $u=Ky$ such that the matrix $A+BKC$ has all its eigenvalues in the complex left half plane and, if such a feedback does not exist, to prove that it does not. Substantial progress has not been made on the computational aspect of the solution to this problem. In this paper we consider instead `which annihilating polynomials can a matrix of the form $A+BKC$ possess?'. We give a simple solution to this problem when the system has either a single input or a single output. For the multi input - multi output case, we use these ideas to characterize the annihilating polynomials when $K$ has rank one, and suggest possible computational solutions for general $K.$ We also present some numerical evidence for the plausibility of this approach for the general case as well as for the problem of shifting the eigenvalues of the system. 24 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|